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Significato geometrico di Derivata Definition of Derivative

To understand the geometric meaning of the derivative as well must be able to find the tangent to a curve at a point:
Taking a curve we set a point P and then another point P 'other than P and draw the straight line PP 'that's enough to slide P' on the curve towards P and when P 'will be identical to P we have the tangent to the curve at P (I traced the rays instead of straight lines to make more' simple picture)
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Definition: defining tangent to a curve in a position limit of the line from behind a rope to tighten the rope on the second point primo
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Ora se riprendiamo la definizione di derivata, vedi che quando h tende a zero il secondo punto sulla curva si sposta verso il primo punto fino a coincidere
inoltre il rapporto incrementale e' uguale al coefficiente angolare della retta che congiunge i due punti sulla curva.
Quindi, al limite, la derivata ed il coefficiente angolare della retta tangente alla curva devono coincidere cioe':
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Definizione: la derivata di una funzione in un punto e' uguale al coefficiente angolare della retta tangente alla funzione in quel punto



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really need to make a small clarification here: the tangent and 'always on one side while the derivative of the curve is on a chord of the curve: ie 'the derivative and the slope of the tangent for something different, but something so small (infinitesimal) to affect the calculations, however, talking about the return on this concept of differential